Actually, it's the other way around. The Iron Islands are one of the Seven Kingdoms, but the Riverlands are not. Since the Riverlands were ruled by another kingdom by the time they were conquered by Aegon the First, they were never officially regarded as a kingdom in their own right at the point where Game of Thrones takes place.
As fire as the books go the riverlands and the iron islands are all one kingdom referred to as "the kingdom of the rivers and the isles", or something along those lines, but the riverlands is certainly considered the more important part of the kingdom and is most usually referred to as the 7th kingdom, while the iron islands has a similar status to the crownlands
Hopefully this clears up any confusion